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Quantitative Characterization of Brain Tissue Alterations in Brain Cancer Using Fractal, Multifractal, and IPR
Mousa Alrubayan1, Santanu Maity1, Prabhakar Pradhan1
1Department of Physics and Astronomy, Mississippi State University, Mississippi State, MS, USA, 39762.
Arxiv
|December 19, 2025
Summary
This study introduces a multiparametric framework combining fractal analysis and Inverse Participation Ratio (IPR) analysis for improved brain cancer detection. These methods accurately characterize tissue microstructure, aiding in early diagnosis and differentiation of healthy from diseased tissues.
Area of Science:
- Neuroscience
- Biophysics
- Computational Biology
Background:
- Accurate characterization of brain tissue microstructure is essential for early cancer detection and diagnosis.
- Existing methods may lack the sensitivity to detect subtle structural alterations indicative of disease.
Purpose of the Study:
- To develop and validate a multiparametric framework for analyzing structural alterations in brain tissues.
- To enhance the differentiation between healthy and cancerous brain tissues using advanced analytical techniques.
Main Methods:
- Application of box-counting methods on brightfield microscopy images to estimate fractal dimension (Df).
- Utilizing fractal functional transformation, multifractal analysis (f(α) vs α curves), and Inverse Participation Ratio (IPR) analysis.
- Combining fractal dimension (Df), logarithmic forms (ln(Df), ln(Dtf)), multifractal spectra, and IPR for a comprehensive assessment.
Main Results:
- Fractal dimension (Df) and its logarithmic forms showed distinct distributions between healthy and cancerous tissues.
- Functional logarithmic fractal dimension (ln(Dtf)) significantly improved differentiation by highlighting local structural variations.
- Multifractal analysis revealed increased heterogeneity in cancerous tissues, indicated by broader f(α) vs α curves.
- IPR analysis demonstrated higher structural disorder and nanoscale variations in mass density in cancer tissues.
Conclusions:
- The combined multiparametric framework offers a robust approach for measuring tissue complexity.
- This framework holds significant potential for improving microscopic diagnostic methods for brain cancer detection.
- The study highlights the utility of fractal-based and IPR analyses in understanding tissue microstructure for diagnostic purposes.
